#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int dlatdf_(integer *ijob, integer *n, doublereal *z__, 
	integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal, 
	integer *ipiv, integer *jpiv)
{
/*  -- LAPACK auxiliary routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    DLATDF uses the LU factorization of the n-by-n matrix Z computed by   
    DGETC2 and computes a contribution to the reciprocal Dif-estimate   
    by solving Z * x = b for x, and choosing the r.h.s. b such that   
    the norm of x is as large as possible. On entry RHS = b holds the   
    contribution from earlier solved sub-systems, and on return RHS = x.   

    The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q,   
    where P and Q are permutation matrices. L is lower triangular with   
    unit diagonal elements and U is upper triangular.   

    Arguments   
    =========   

    IJOB    (input) INTEGER   
            IJOB = 2: First compute an approximative null-vector e   
                of Z using DGECON, e is normalized and solve for   
                Zx = +-e - f with the sign giving the greater value   
                of 2-norm(x). About 5 times as expensive as Default.   
            IJOB .ne. 2: Local look ahead strategy where all entries of   
                the r.h.s. b is choosen as either +1 or -1 (Default).   

    N       (input) INTEGER   
            The number of columns of the matrix Z.   

    Z       (input) DOUBLE PRECISION array, dimension (LDZ, N)   
            On entry, the LU part of the factorization of the n-by-n   
            matrix Z computed by DGETC2:  Z = P * L * U * Q   

    LDZ     (input) INTEGER   
            The leading dimension of the array Z.  LDA >= max(1, N).   

    RHS     (input/output) DOUBLE PRECISION array, dimension N.   
            On entry, RHS contains contributions from other subsystems.   
            On exit, RHS contains the solution of the subsystem with   
            entries acoording to the value of IJOB (see above).   

    RDSUM   (input/output) DOUBLE PRECISION   
            On entry, the sum of squares of computed contributions to   
            the Dif-estimate under computation by DTGSYL, where the   
            scaling factor RDSCAL (see below) has been factored out.   
            On exit, the corresponding sum of squares updated with the   
            contributions from the current sub-system.   
            If TRANS = 'T' RDSUM is not touched.   
            NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL.   

    RDSCAL  (input/output) DOUBLE PRECISION   
            On entry, scaling factor used to prevent overflow in RDSUM.   
            On exit, RDSCAL is updated w.r.t. the current contributions   
            in RDSUM.   
            If TRANS = 'T', RDSCAL is not touched.   
            NOTE: RDSCAL only makes sense when DTGSY2 is called by   
                  DTGSYL.   

    IPIV    (input) INTEGER array, dimension (N).   
            The pivot indices; for 1 <= i <= N, row i of the   
            matrix has been interchanged with row IPIV(i).   

    JPIV    (input) INTEGER array, dimension (N).   
            The pivot indices; for 1 <= j <= N, column j of the   
            matrix has been interchanged with column JPIV(j).   

    Further Details   
    ===============   

    Based on contributions by   
       Bo Kagstrom and Peter Poromaa, Department of Computing Science,   
       Umea University, S-901 87 Umea, Sweden.   

    This routine is a further developed implementation of algorithm   
    BSOLVE in [1] using complete pivoting in the LU factorization.   

    [1] Bo Kagstrom and Lars Westin,   
        Generalized Schur Methods with Condition Estimators for   
        Solving the Generalized Sylvester Equation, IEEE Transactions   
        on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.   

    [2] Peter Poromaa,   
        On Efficient and Robust Estimators for the Separation   
        between two Regular Matrix Pairs with Applications in   
        Condition Estimation. Report IMINF-95.05, Departement of   
        Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.   

    =====================================================================   


       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c_n1 = -1;
    static doublereal c_b23 = 1.;
    static doublereal c_b37 = -1.;
    
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2;
    doublereal d__1;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    static integer info;
    static doublereal temp, work[32];
    static integer i__, j, k;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    extern doublereal dasum_(integer *, doublereal *, integer *);
    static doublereal pmone;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *), daxpy_(integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *);
    static doublereal sminu;
    static integer iwork[8];
    static doublereal splus;
    extern /* Subroutine */ int dgesc2_(integer *, doublereal *, integer *, 
	    doublereal *, integer *, integer *, doublereal *);
    static doublereal bm, bp;
    extern /* Subroutine */ int dgecon_(char *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *, 
	    integer *);
    static doublereal xm[8], xp[8];
    extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, 
	    doublereal *, doublereal *), dlaswp_(integer *, doublereal *, 
	    integer *, integer *, integer *, integer *, integer *);
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]


    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --rhs;
    --ipiv;
    --jpiv;

    /* Function Body */
    if (*ijob != 2) {

/*        Apply permutations IPIV to RHS */

	i__1 = *n - 1;
	dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);

/*        Solve for L-part choosing RHS either to +1 or -1. */

	pmone = -1.;

	i__1 = *n - 1;
	for (j = 1; j <= i__1; ++j) {
	    bp = rhs[j] + 1.;
	    bm = rhs[j] - 1.;
	    splus = 1.;

/*           Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and   
             SMIN computed more efficiently than in BSOLVE [1]. */

	    i__2 = *n - j;
	    splus += ddot_(&i__2, &z___ref(j + 1, j), &c__1, &z___ref(j + 1, 
		    j), &c__1);
	    i__2 = *n - j;
	    sminu = ddot_(&i__2, &z___ref(j + 1, j), &c__1, &rhs[j + 1], &
		    c__1);
	    splus *= rhs[j];
	    if (splus > sminu) {
		rhs[j] = bp;
	    } else if (sminu > splus) {
		rhs[j] = bm;
	    } else {

/*              In this case the updating sums are equal and we can   
                choose RHS(J) +1 or -1. The first time this happens   
                we choose -1, thereafter +1. This is a simple way to   
                get good estimates of matrices like Byers well-known   
                example (see [1]). (Not done in BSOLVE.) */

		rhs[j] += pmone;
		pmone = 1.;
	    }

/*           Compute the remaining r.h.s. */

	    temp = -rhs[j];
	    i__2 = *n - j;
	    daxpy_(&i__2, &temp, &z___ref(j + 1, j), &c__1, &rhs[j + 1], &
		    c__1);

/* L10: */
	}

/*        Solve for U-part, look-ahead for RHS(N) = +-1. This is not done   
          in BSOLVE and will hopefully give us a better estimate because   
          any ill-conditioning of the original matrix is transfered to U   
          and not to L. U(N, N) is an approximation to sigma_min(LU). */

	i__1 = *n - 1;
	dcopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
	xp[*n - 1] = rhs[*n] + 1.;
	rhs[*n] += -1.;
	splus = 0.;
	sminu = 0.;
	for (i__ = *n; i__ >= 1; --i__) {
	    temp = 1. / z___ref(i__, i__);
	    xp[i__ - 1] *= temp;
	    rhs[i__] *= temp;
	    i__1 = *n;
	    for (k = i__ + 1; k <= i__1; ++k) {
		xp[i__ - 1] -= xp[k - 1] * (z___ref(i__, k) * temp);
		rhs[i__] -= rhs[k] * (z___ref(i__, k) * temp);
/* L20: */
	    }
	    splus += (d__1 = xp[i__ - 1], abs(d__1));
	    sminu += (d__1 = rhs[i__], abs(d__1));
/* L30: */
	}
	if (splus > sminu) {
	    dcopy_(n, xp, &c__1, &rhs[1], &c__1);
	}

/*        Apply the permutations JPIV to the computed solution (RHS) */

	i__1 = *n - 1;
	dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);

/*        Compute the sum of squares */

	dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);

    } else {

/*        IJOB = 2, Compute approximate nullvector XM of Z */

	dgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
		info);
	dcopy_(n, &work[*n], &c__1, xm, &c__1);

/*        Compute RHS */

	i__1 = *n - 1;
	dlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
	temp = 1. / sqrt(ddot_(n, xm, &c__1, xm, &c__1));
	dscal_(n, &temp, xm, &c__1);
	dcopy_(n, xm, &c__1, xp, &c__1);
	daxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
	daxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
	dgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
	dgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
	if (dasum_(n, xp, &c__1) > dasum_(n, &rhs[1], &c__1)) {
	    dcopy_(n, xp, &c__1, &rhs[1], &c__1);
	}

/*        Compute the sum of squares */

	dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);

    }

    return 0;

/*     End of DLATDF */

} /* dlatdf_ */

#undef z___ref


